Monday, August 27, 2012

This is the other paper I wrote for the Buddhist Philosophy class, much in the same vein as the previous one. I didn't feel like I could move on to the content of the arguments in the texts without better understanding the manner of argument or reasoning. I still have a lot of work to do in that regard!

John Emmer

Buddhist Philosophy

Prof. Sumana Ratnayaka

SIBA, August, 2012

The Logic of the First
Debate in the Kathāvattu

According
to A.K. Warder, “In the Kathāvattu. . . we have the
earliest known Indian philosophical work which proceeds on the basis
of a set of established logical techniques” (287). If this is
so, the arguments of the Kathāvattu might therefore lend
themselves to representation in common systems of symbolic logic.
However, scholars have differed over the best way to to this. If we
attempt to represent the arguments in the Kathāvattu in terms of
western symbolic logic, what is the best way to do so? How can we
best represent the arguments of the text in a way that is revelatory
about our best understanding of their true meaning? I will look at a
few such attempts to represent the first argument of the text and
discuss their relative merits.

First, let us look at the initial argument, which represents an
exchange between a Theravādin and a Puggalavādin
('personalist', or someone who believes in a persisting soul, self,
or person). As translated by Aung and Rhys Davids, the exchange is
as follows:

Th: Is 'the person' known in the sense of a real and ultimate fact?

Pg: Yes.

Th: Is the person known in
the same way as a real an
ultimate fact is known?

Pg: Nay, that cannot truly be said.

Th: Acknowledge your refutation: If the person be known in the sense
of a real and ultimate fact, then indeed, good sir, you should also
say, the person is known in the same way as [any other] real and
ultimate fact [is known].

. . .In affirming the former statement, while denying the latter, you
are wrong.

(Italics and brackets in original, 8-9)

Kalupahana renders the same passages as:

Th: Is a person obtained
as an absolute truth, as an ultimate reality?

Pg: Yes.

Th: Is a person, as an absolute
truth, as an ultimate reality, obtained
in the same way that an absolute truth, an ultimate reality, is
obtained?

Pg: One should not say so.

Th: Admit your refutation.

If you say that a person is
obtained as an absolute truth,
as an ultimate reality, then you should also say that a person is
obtained as an absolute truth,
as an ultimate reality, in the same way that an absolute truth, an
ultimate reality, is obtained.

. . . What you state [, that one 'should say' the former and 'not
say' the latter,] . . . is wrong.

(Italics in original, brackets mine, 134)

I will compare three representations of this argument and see if we
can find reason to choose one over the others, or if perhaps there is
yet another preferred alternative.

I. The term-logical representation of Aung and Bochenski.

Matilal reconstructs the term-logical representation (the variables
range over terms, not propositions) of the argument from Aung and
Bochenski as follows:

In this representation, 'A' is 'the person', 'B' is the
characteristic of being found as a “real and ultimate fact”
or “as an absolute truth, as an ultimate reality”, and
'C' is the characteristic of being found in the same way as other
such realities are found - or in Kalupahana's account as any
such reality would be found (more on this later). Although
this representation does not match the structure of the presentation
of the argument from the text, it does seem to me on its face to well
represent the logical structure of the argument itself. That is,
there are clearly three distinct 'terms' being compared in the text,
and this logical formulation captures that fact and the stated
relations of those terms well.

II. Jayatilleke's propositional representation.

Jayatilleke claims that the term-logical account misrepresents and
obfuscates the argument (414-415), stating that it is better to
represent the argument using simple propositions as:

p

~q

p → q

├ ~p

(413)

Here p represents the assertion that 'the person is found as
an ultimate reality' and q represents that 'the person is
found in the same was as other/any ultimate realities'. As
Jayatilleke argues, this representation indeed has the advantage of
matching more closely the presentation of the argument in the text
(414-415). That is, the Puggalavādin is depicted first as
assenting to p, then denying q, at which point the
Theravādin asserts the connection between the two claims in
order to refute the Puggalavādin's initial claim. Jayatilleke
also argues that the Kathāvattu, like “the Buddhist
tradition as a whole” considers propositions as wholes rather
than breaking them down into terms (313, 414). However, even if that
be the case, the reduction of the statements to bare propositions
rather than term comparisons seems to me to obscure the nature of the
argument.

Matilal argues that the distinctive characteristic of “Indian
logic” as opposed to “Western logic” is that the
former includes epistemological issues, where the latter excludes
them (14). That is to say, the Indian approach did not emphasize the
distinction between formal validity and argumentative soundness:

It is now-a-days claimed that a logician's concern is with the
validity of inference, not with its soundness, which may depend on
extra-logical factors (the truth of the premises). This is the ideal
in [Western] formal logic. In India, however, this distinction was
not often made, for the philosophers wanted their “logically”
derived inferences or their conclusions also to be pieces of
knowledge. Thus, validity must be combined with truth. (17)

He
points out that a commonly used example in modern scholarly writing
about Indian reasoning, “Wherever there is smoke, there is
fire. There is smoke on the yonder hill. Therefore there is fire
there,” when presented in the ancient Indian texts was actually
formulated as “The hill is fire-possessing. Because it is
smoke-possessing. For example, the kitchen”
[emphasis added] (15-16). The Indian formulation has an example
demonstrating the smoke to fire relation as a central element of the
argument, relying on the analogy to the kitchen for the soundness of
the argument. If we accept this epistemological character of Indian
logic, then we may conclude that Jayatilleke's propositional
representation of the argument obscures the important fact that it is
indeed terms that are being compared. The Theravādin is arguing
that, once the Puggalavādin places the person in the category of
ultimate truths, he should also accept that the person should have
the other characteristics commonly associated with those truths –
in this first case, how they are known. It is significant in this
regard that the text continues on to compare the person to many other
'things known' and how they are known. Jayatilleke's representation
of the argument obscures this comparative or analogical
characteristic of the debate.

III.
Kalupahana's analysis of the argument

While
Kalupahana agrees with Jayatilleke that only two variables are needed
to represent the argument, and therefore that the propositional form
captures the structure
of the argument, he claims that both of these interpretations miss
the actual content of
the argument (134-136). Kalupahana suggests that, rather than p
and q,we would be
better served by seeing the propositions as

pTR (person in truth and
reality) and

TR (truth and reality)

(135).

Here
the full forms of these statements are given by Kalupahana as pTR:
“A person is obtained as an absolute truth, as an ultimate
reality” and TR: “An absolute truth, an ultimate reality,
is obtained” (135). In terms of the logical structure,
Kalupahana would presumably agree with Jayatilleke's representation,
so long as the substitutions of pTR
and TR for p and q
respectively have been made, giving:

pTR

~TR

pTR
→ TR

├ ~pTR

But
he argues that both the accounts we have looked at miss the actual
point of the argument. Kalupahana calls out two aspects of the text
that are not directly addressed in the other two accounts.

First,
which we have already alluded above, is his claim that the
Theravādin's second proposition, q
or 'A is C' or TR, is referring to the possibility of
attaining any absolute truth or ultimate reality
as opposed to comparing the nature of the person to other
accepted absolute truths. His
claim is that all the scholars we have looked at so far were mislead
by Buddhaghosa's interpretation of the Theravādin's second
question (135). Buddhaghosa's commentary interprets: “'In the
same way,' that is either as the factors of mind and body are
known, by immediate
consciousness, or under one of the twenty-four relation-categories”
(emphasis added, Aung 9n2)2.
Kalupahana's claim to the contrary is that the Theravādin is
actually asking whether any
ultimate reality can be obtained, and in this regard that the
peculiar nature of the Puggalavādin's reply is also significant.
This is his second distinction, that the Puggalavādin's “One
should not say so” is not a simple negation of a proposition,
but rather a claim that the category of ultimate reality is
unspeakable:

Both seem to assert that one should
not speak (na vattabbe)
of an absolute truth or ultimate reality (TR). Yet the Personalist
proceeds to assert a person as an absolute truth, as an ultimate
reality (pTR), while
the Theravādin does not. . . . This means that the Personalist
believes that “what cannot be spoken of” (na
vattabbe) can still be obtained
or experienced, whereas the Theravādin insists that what is
unspeakable is also not obtained or experienced. (136-137)

In
Kalupahana's view, the Puggalavādin and Theravādin are both
closer to his interpretation of early Buddhist non-essentialism than
the tradition has either of them, for in his view they both agree to
the unspeakable nature of the absolute, whereas the tradition has
them arguing over what phenomena fit in the category of the absolute,
with the battle against absolutism having already been lost or
abandoned.

Kalupahana
believes that Buddhaghosa “advertently or inadvertently”
introduced “absolutist or substantialist distinctions. . . into
the Theravāda tradition” (133). Because the Theravāda
tradition subsequently takes the Abhidhamma to be dealing in
'ultimate truths', when Buddhaghosa compares the 'way the person is
known' to the way these other specific truths are known, it leads to
the conclusion that the Theravādin of the Kathāvattu is
asking the Puggalavādin to compare his knowing of the person to
the accepted knowing of these other 'ultimate truths'. On the
contrary, Kalupahana argues that it is the very Kathāvattu that
evidences against this interpretation of the Abhidhamma, as “No
one reading the excessively long debate in the Kathāvattu on the
conception of a person can assert that the Abhidhamma deals with
ultimate realities (paramattha)”
(145). However, the Theravādin does
to assert that 'material quality' is known as a 'real and ultimate
fact' as well as the rest of the fifty-seven 'ultimates'. For
example, take the following question posed by the Theravādin:
“Material quality [rūpaṃ (Aung
15n3)] is (you have admitted) known as a real and ultimate fact.
Feeling, too, is known as such. Now, is material quality one thing
and feeling another?” (17) Assuming we have an adequate
translation, it is clear in this passage that the Theravādin is
indeed assenting to there being 'real and ultimate facts', for he
states that feeling “is known as such” rather than asking
whether it is. One could still argue about the nature of 'real and
ultimate facts'. For example, are they absolutes, independent of
human experience, or just inevitable aspects of human experience?
But Kalupahana's position rests on the assertion that the comparison
to these other facts is not being made in the first argument, whereas
the rest of the text, independent of Buddhaghosa's analysis, would
seem to indicate that the comparison is indeed intended.

Conclusion

Given
the limitations I have outlined for the representations provided by
Jayatilleke and Kalupahana, but acknowledging Jayatilleke's argument
that the original term-logical representation obscures the structure
of the debate as presented in the text, I think the best
representation may therefore be a term-logical representation
rearranged to match the presentation in the text, that is:

Pg: A is B

Pg: ~(A is C)

Th: (A is B) → (A is C)

Th: ├ ~(A is B)

Here
we have the Puggalavādin first assenting to the person (A) being
an ultimate reality (B), but not being known in the way of other
ultimate realities (C), followed by the Theravādin's assertion
that the former implies the latter and therefore that the
Puggalavādin's original assertion cannot stand alongside his
second.

This
could perhaps be made more clear by rendering it in predicate logic:

Pg: (Ǝx)(Px · Rx) “Some person is known as a reality.”Pg: ~(Ǝx)(Px · Kx)3 “No person is known in the way other realities are known.”Th:
(x)(Rx → Kx) “All realities are known in the way other
realities are known.”Th: ├ ~(Ǝx)(Px · Rx) “Therefore no person is known as a reality.”

This
rendering has the advantage of making the Theravādin's argument
more clear in that the third statement is more suggestive of why the
Puggalavādin's statements are contradictory. However, all we
have in the text are statements to the effect of “if you say
the person is known as a reality, you should say it is known in the
way other realities are known”, so the Theravādin could in
fact have reasons other than the belief that all realities must be
known in the same way for making this assertion. Also, to be more
accurate, we should probably introduce a particular for the known
person, for it is not clear that the Puggalavādin is arguing
about any notion of a
person as opposed to merely making claims about his own notion of
such.

Because
the predicate rendering opens up these additional questions, it is
perhaps best not to recommend it without further analysis of the rest
of the comparative arguments made in the text. For the present
therefore I propose the rearranged term-logical rendering as
preferable to the alternatives presented in the texts examined here
and leave the question of the predicate rendering for future study.

1 Matilal claims (37) that this is Aung's representation, but Aung's representation has four terms (If A is B then C is D; But C is not D; Therefore A is not B (xlviii)). Matilal says Bochenski “gave an improved version of the same” (37), and Jayatilleke says that Bochenski “seeks to reinstate” Aung's account but improves on it by using only three terms instead of four (Jayatilleke, 412 and n.4).Therefore, having been unable to obtain a copy of Bochenski to check for this paper, I am relying on Matilal's representation of the argument as being equivalent to that by Bochenski (against which Jayatilleke frames his discussion.)

2 Law's translation of this passage is “'In the same way'. . .here it means. . . 'Is the 'person' got at in the same way as a real and ultimate object is got at, because of its having either material form and the like, or because of the relation-categories and the like?'” (11).

3 Suber suggests (tip 18) that this would be better rendered as “(x)(Px → ~Kx)” (and similarly for the fourth statement), but I think the rendering I give here is easier to read as the English statements I have provided to approximate the claims as they are made in the text. Also, the existential rendering of the fourth statement is easier to see as the direct negation of the Puggalavādin's initial assertion, whereas the universal rendering requires a little more understanding of predicate logic on the part of the reader.

Works Cited

Aung,
Shwe Zang and Mrs. Rhys Davids. Points
of Controversy, or, Subjects of Discourse: Being a translation of the
Kathāvattu from the Abhidhammapiṭaka.
1915. Oxford: Pali Text Society, 1993.

Here is the first of my real papers for any of my classes here. Don't expect any profound insights that will move you very far along the path to Awakening - unless of course that path for you travels through an attempt to understand certain logical patterns in Early Buddhist writings...

John Emmer

Buddhist Philosophy

Prof. Sumana Ratnayaka

SIBA, August, 2012

The Fourfold Analysis of
Predication in Early Buddhism

A
certain fourfold pattern of propositions, or rather perhaps a certain
family of fourfold
propositions, appears often in the Pali Canon. An example from one
of the debates in the Kathāvattu follows:

Theravādin: Does (a person or) soul run on (or transmigrate)
from this world to another and from another world to this?

Puggalavādin: Yes.

Th: Is it the identical soul who transmigrates from this world to
another and from another world to this?

Pg: Nay, that cannot truly be said .
. . (complete as above)

Th: Then is it a different soul that transmigrates. . . .

Pg: Nay, that cannot truly be said.
. . . (complete as above)

Th: Then is it both the identical and also a different soul who
transmigrates . . . ?

Pg: Nay, that cannot truly be said. . . .

Th: Then is it neither the identical soul, nor yet a different soul
who transmigrates . . . ?

Pg: Nay, that cannot truly be said. . . .

Th: Then is it the identical, a different, both identical and also
different, neither identical, nor different soul who transmigrates .
. . ?

Pg: Nay, that cannot truly be said. . . .

(ellipses and italics in original, Aung 26-27)

This example actually contains five options, as the standard four are
combined for the fifth. Kalupahana symbolizes the four alternatives
as:

S is P

S is ~P

S is (P · ~P)

S is ~(P · ~P)

(17)

Symbolized in this manner, the
scheme seems to contain an obvious contradiction (III) and a
tautology (IV), making those two statements useless to consider, let
alone whatever it might mean to assert all of them together. What
sense then can we make of this scheme?

Not
everyone has assumed that one could
make sense of these propositions. For example, Poussin
takes them to be a “four-branched dilemma” that indeed
violates the law of contradiction (Jayatilleke 333). This
interpretation is extremely unfair to the source material, and does
not bear up under even the slightest investigation. However, it is
easy to see how one could reach this conclusion if one uses a
symbolization like that given above. Jayatilleke therefore offers
the following alternative notation and explains how it better
represents how the fourfold propositions are used:

S is P

S is notP

S is P.notP

S is not P.notP

(136 136n2)

The
point of his 'notP' notation as opposed to '~P' is to represent
that P and notP are contrary propositions rather than
contradictory ones. He gives the example of pleasure and pain: if
'S is P' (I) is interpreted as 'he experiences pleasure', then 'S
is notP' (II) may mean 'he experiences pain', which is not the
same as 'he does not experience pleasure', since a person could
experience pleasure in one part of the body while experiencing
pain in another at the same time, which can be understood as the
meaning of 'S is P.notP' (III) (341)1.
This distinction successfully saves the scheme from outright
contradiction. However, Jayatilleke goes on to say that 'S is not
P.notP' (IV) then represents “the person whose experiences
have a neutral hedonic tone, being neither pleasurable nor
painful” (341). This brings us to a problem I have with the
both Kalupahana's and Jayatilleke's symbolization of the fourth
proposition. I do not understand why they both use conjunction
here rather than disjunction.

Kalupahana's
symbolization follows an example where he gives a statement of type
IV from the Canon as “The world is both neither eternal nor not
eternal” (49) and Jayatilleke's Canonical example
is “this world is neither finite nor infinite” (340),
which corresponds well to the example of a person experiencing
neither pleasure nor pain. However, Kalupahana's “S is ~(P · ~P)” surely means “the world is not both
eternal and not eternal” and Jayatilleke's “S is not
P.notP” surely means “the world is not both
finite and infinite” or “he does not
experience both
pleasure and pain”. A better symbolization of the fourth
proposition would therefore be “S is ~(P v ~P)” for
Kalupahana's scheme or “S is not (P v notP)” in
Jayatilleke's2.
This symbolization matches statements like “the world is
neither finite nor infinite”.

Not
only does the symbolization with disjunction match the example
English statements of both authors better, but it also provides a
stronger alternative to the third proposition. The symbolizations of
both Kalupahana and Jayatilleke for IV simply negate III, leaving a
statement that could be asserted in conjunction with either I or II
without contradiction. For example, it is not contradictory to state
both “he does not
experience both
pleasure and pain” and “he experiences pleasure”,
so long as he is not also experiencing pain. But if I say, for IV,
“he experiences neither
pleasure nor pain”,
then I cannot at the same time assert any of the other propositions
without contradiction. This would seem to be valuable for
Jayatilleke, who claims that, for the early Buddhists, “when
one alternative was taken as true, it was assumed that every one of
the other alternatives were false” (346). I have presented
these alternatives with their truth tables in the appendix to make
the truth relationships between the alternative propositions clear.

However,
even with the improved symbolization, we could still assert III with
I or II, since III would seem merely to state that both I and II are
true (again, see the appendix if this is not clear). Jayatilleke
therefore provides an example from the Dīgha Nikāya showing
that I and II should be taken as universal propositions incompatible
with III or IV (340). The following is Walshe's translation
of the passages in question (to disentangle the presentation of the
example from Jayatilleke's discussion of it):

[One thinks:] “I dwell perceiving the world as finite.
Therefore I know that this world is finite and bounded by a circle.”

[Another thinks:] “I dwell perceiving the world as infinite.
Therefore I know that this world is infinite and unbounded.”

[Yet another thinks:] “I dwell perceiving the world as finite
up-and-down, and infinite across. Therefore I know that the world is
both finite and infinite.”

[A
fourth] Hammering it out by reason, he argues: “This world is
neither finite nor infinite. Those who say it is finite are wrong,
and so are those who say it is infinite, and those who say it is
finite and infinite.
This world is neither finite nor infinite.”

(numbers and brackets mine, 79 DN I.22-23)

First we note that III here provides a Canonical example of the
non-contradictory nature of the alternatives from I and II. Just as
a person can experience pain in some part of the body and pleasure in
another simultaneously, the third proposition here claims that the
world could be finite in some dimensions while being infinite in
others. However, what Jayatilleke really wants to call attention to
here is the explicit universalization of the first two claims. The
first claimant asserts that the world is “bounded by a circle”,
or in Jayatilleke's translation, “bounded all around”
(340). This rules out the possibility of there being a simultaneous
infinitude for any dimension. Likewise, the second claimant's “unbounded” assures us that there
is no dimension that is not infinite. If this universal nature of
the first two statements and limitation in the third is present in
all instances of the fourfold analysis, then combined with our
improved understanding of the fourth statement, we do indeed have a
mutually-exclusive set of propositions.

There
is another important aspect of the previous example that Jayatilleke
highlights. Notice that in the first three statements, the
claimant's knowledge is said to be based on direct perception of
reality. But the fourth claimant is said to have reached his
conclusion “hammering it out by reason”. Jayatilleke
compares this point of view to Kant's position, after demonstrating
in the Antinomies that both the finitude and inifinitude of the world
could be proved with pure reasoning, that
one must therefore conclude that neither characteristic is
appropriately predicated of the world (341). The fourth claimant
does not directly perceive the truth of his claim because in his view
the terms just do not make sense in experience. Presumably there is
no experience corresponding to 'unpredicatability' – one must
simply reason it out.

Our
understanding of the fourfold analysis so far is that the first
two propositions represent contrary but not contradictory universal
predications, the
third proposition represents limited predications of both contraries,
and the fourth represents the position that the predications in
question are meaningless or otherwise inapplicable.
We have also noted that at most one of the four
propositions is to be asserted by anyone claiming consistency.
In addition, however, Jayatilleke points out that there
are times where all four alternatives can either be rejected or
negated.

To
reject the
alternatives as opposed to negating
them is typically represented in the Canon by phrases like “mā
h'evaṃ” or “do not say so” as opposed to
something like “na h'idaṃ” or “it is
not so” (Jayatilleke 346-347). According to Jayatilleke, the
former case is found when one confronts a “meaningless
question”, such as “is there anything else after complete
detachment from and cessation of the six spheres of experience?”
(346) When confronted with the four variations of this question,
Sāriputta replies with “mā h'evaṃ” to
them all (AN.II.161 cited in Jayatilleke 346). This is a well-known
tactic used elsewhere in the Canon as well, where the Buddha is known
to have refused to answer certain classes of questions. Note also
that in the first example provided above, the Puggalavādin
responds to each of the alternatives with “that cannot truly be
said”.

More
problematic is the case where all four alternatives are negated,
since according to our truth table analysis, there is no set of truth
conditions under which all four alternatives are false (see
appendix). Jayatilleke claims that this is equivalent to the problem
that Aristotelian logic has with a question like “have you
given up smoking?” when asked of a non-smoker (347). The
simple answer to this seems to be “no”, unless one adds a
premise that anyone who has not given something up is actually still
engaged in that practice. Otherwise I am quite happy to say that I
have not given up a practice that I have also never started. Even
so, I don't see why the Aristotelian could not also reply “one
should not say so”, refusing to give the statement a truth
value in the same way the early Buddhist might reject a meaningless
question.

The
example Jayatilleke provides for the fourfold negation provides us
with another problem. The example is this:

Is
it the case that one attains the goal by means of knowledge?

Is
it the case that one attains the goal by means of conduct?

Is
it the case that one attains the goal by means of both knowledge and
conduct?

Is
it the case that one attains the goal without knowledge and conduct?

(347)

Assertions I, II, and III seem to fit the proposed interpretation of
the fourfold scheme, but what are we to make of the phrase “without
knowledge and conduct” in assertion IV? Do we have here a case
of Jayatilleke's “S is not P.notP” as opposed to our
preferred “S is not (P v notP)”? It is hard to say
without a better understanding of the original Pali, an understanding
which I do not yet possess. Jayatilleke does however provide us with
a useful explanation of how all these alternatives could be denied:
knowledge and conduct are necessary but not sufficient conditions for
the goal (347). But this does not help us resolve the problem with
the truth-functional representation of the statements (i.e. that
there is no set of truth conditions under which they can all be
false).

This
is probably as far as I can go without a better knowledge of Pali
which would enable me to more carefully examine the occurrences of
the fourfold schema in the Canon. Also, many more examples would
need to be analyzed to determine the applicability of the given
interpretation (summarized in the heavily italicized paragraph on
page 5). For the time being, however, I am willing to assert that
this interpretation, as developed primarily by Jayatilleke but with
slight modifications by me, is a good “rule of thumb” for
approaching instances of the fourfold schema in the
Canon. It is certainly better than declaring the texts to be
contradictory and tautological. It provides patterns and angles that
one can look for in the texts that help in understanding the
arguments being made. Perhaps in the future, with a greater
understanding of Pali, I can return to these texts and improve upon
the analysis.

Appendix: Truth-Table Analysis

I

II

III

IVa

IVb

IVc

P

notP

P

·

notP

~

(

P

·

notP

)

~

(

P

v

notP

)

~

P

·

~

notP

A

T

T

T

T*

T

F

T

T

T

F

T

T

T

F

T

F

F

T

B

T*

F

F

F

F

T

T

F

F

F

T

T

F

F

T

F

T

F

C

F

T*

F

F

T

T

F

F

T

F

F

T

T

T

F

F

F

T

D

F

F

F

F

F

T*

F

F

F

T*

F

F

F

T

F

T*

T

F

The table above is provided to illustrate the superiority of my
proposed rendering of the fourth proposition as IVb (or
its logical equivalent of IVc)
as well as to simply make more clear the relation of the truth values
of the four propositions. If we are to maintain the criterion that
the truth of any one of the four propositions implies the falsity of
the other three, then each row (A, B, C, and D) should only have a
'T' in the column representative of the propositional truth value
(indicated by the placement of the column headers) for exactly one of
the four propositions (I, II, III, or IV). These mutually exclusive
alternatives are represented with asterisks.

Row A violates the criterion if we do not consider the special
qualification for P and notP when used in I and II such that they are
universal here but not in III or IV. To represent this, I have
presented the 'T' values in I.A and II.A with strike-through, leaving
the only proposition which asserts them both as true III.A.

The superiority of IVb and IVc over IVa is shown by the presence of strike-through
in cells IVa.B and IVa.C which
would violate the exclusivity criterion without some further
reasoning for why they should be treated in some special manner to
prevent one from saying, for example, that the universe is finite in
all respects (I.B) and also that it is finite in some respects but
not infinite in any respects (IVa.B). The latter
proposition could be interpreted as either equivalent to the former
in that 'some' could be equivalent to 'all', or could be taken to
mean that the universe is finite in some respects and infinity cannot
be predicated of the universe. This could of course be clarified
through the use of a predicate logic with quantifiers (which is
perhaps the preferable solution since this would also forgo the need
for the special strike-through annotation in I.A and II.A) but as
long as we are keeping to simple propositional logic it is easier to
just use IVb or IVc rather than IVa.

1 Jayatilleke is talking about sukhī, which he translates as “experiencing pleasure, [or] happy” and then switches between using pleasure/pain and happiness/unhappiness in his examples in a way that suggests questions that need not be relevant in this context (e.g. is happiness the same as pleasure and unhappiness the same as pain?), so I have altered his examples to stick to one translation.

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About Me

This blog is to record my experiences and thoughts as I move to Sri Lanka to study Buddhism. I'm fairly new to Buddhism, only having meditated regularly since the beginning of 2011. But my experience so far, especially on retreats, has convinced me that this path can bring me a level of peace that I had not previously believed was attainable for me. I decided I wanted to spend some time just focusing on the Dhamma, so I've quit my job, and I'm off to Sri Lanka to learn Pali and study the suttas. Follow along if you like, and may you be happy!